A number of hotel rewards credit cards throw in a free night’s stay for cardholders each year. The catch: All of the cards charge an annual fee, and the room may be at a lower- or mid-tier property. Participants include Starwood Preferred Guest from American Express (annual fee: $95), Marriott Rewards Premier Plus ($95), IHG Rewards Club Premier ($89) and Hyatt Credit Card ($75). The Citi Prestige card carries an annual fee of $450, but cardholders have unlimited use of their “fourth night free” benefit by booking a stay of four consecutive nights at almost any hotel by phone through the Citi Prestige “concierge” or at www.thankyou.com.